Historical Volatility Calculator
Solve the annualisation relation σannual = σdaily · √365 for either unit — daily volatility or annualised volatility — with step-by-step math, a clean bell-curve schematic, and companion metrics including the volatility regime grid and implied daily move ranges.
Annualised volatility regimes differ across asset classes. The card matching your current σ is highlighted below, using crypto-scale benchmarks (equities and FX are quieter).
Volatility is standard deviation of returns
Historical volatility is the standard deviation of logarithmic returns over a sample window — typically 30, 60, or 90 days. It quantifies how spread out the returns have been around their mean, not how much the price has moved in any direction. A stock that rises 1% every day has low volatility, not high — even though it is climbing steadily. Volatility is about the size of the swings, not their sign. This is why "volatile" is often used interchangeably with "risky": the bigger the swings, the wider the range of outcomes the market is pricing in.
Why √365 and not 365
Variance — the square of volatility — scales linearly with time. If daily variance is σ_d², then N-day variance is N · σ_d². Volatility is the square root of variance, so N-day volatility is √N · σ_d. The annualisation factor for daily data is therefore √365 ≈ 19.105 (crypto trades 365 days a year). For equities, which trade roughly 252 days a year, the factor is √252 ≈ 15.87. Using the wrong factor is a common and material error: a 2% daily vol annualises to 38.2% under √365 but only 31.7% under √252.
HV is backward-looking; IV is forward-looking
Historical volatility is computed from past returns — it is a factual measurement of what has already happened. Implied volatility is derived from options prices and represents the market's expectation of future volatility. The two usually diverge: when IV is higher than HV, options are expensive and the market is pricing in future turbulence; when IV is lower than HV, options are cheap and the market is complacent. The IV−HV spread is itself a tradable signal, and the "volatility risk premium" is the statistical tendency of IV to exceed HV on average.
Sample window matters a lot
A 30-day window reacts fast to recent turbulence but is noisy and prone to whipsaws. A 90-day window is smoother but lags regime changes by weeks. A 365-day window captures a full annual cycle but can mask recent shifts entirely. Most desks look at multiple windows simultaneously (30, 60, 90) and treat divergence between them as a signal. For crypto in particular, a 30-day window can swing from 30% to 120% annualised within two weeks, so the choice of window is far more consequential than the exact annualisation factor.
How to Use This Calculator
The annualisation relation links two quantities: daily volatility and annualised volatility. Pick which one you want the tool to solve for, then enter the other.
1. Choose what to solve for
Pick σannual or σdaily from the toggle. The calculator rearranges σannual = σdaily · √365 automatically for whichever you choose.
2. Use realistic presets
Presets cover the range: daily vol from 0.3% (major FX) to 8% (small-cap crypto), and annual vol from 10% (quiet large-cap equity) to 200% (extreme altcoin turbulence).
3. Know your trading calendar
This calculator uses √365 — the correct factor for crypto markets that trade every day. For equities and other markets that trade about 252 days per year, use √252 ≈ 15.87 instead, which produces about 17% lower annualised vol for the same daily input.
4. Read the result and verdict
The result card shows the annualised volatility plus the daily input, the √365 factor, and the implied 1σ yearly range. A colour-coded verdict classifies the σ across regimes from quiet to extreme.
5. Check the regime grid and schematic
The regime grid shows where this σ sits relative to low, normal, high, and extreme volatility regimes, with the matching card highlighted. The schematic shows a daily bell curve → √365 arrow → annual bell curve with 1σ bands marked.
6. Switch to Advanced for depth
Advanced mode adds a log-scale daily-vs-annual scaling chart, a sensitivity check on a +1% change in either input, and companion metrics including daily/weekly/monthly σ and the implied 1σ/2σ price ranges at different horizons.
What This Tool Offers
Built around the classic annualisation relation σannual = σdaily · √365, the fundamental bridge between daily and annual volatility.
Two-way conversion
Convert daily volatility to annualised, or annualised back to daily. The calculator applies the exact √365 factor in whichever direction you need.
Clean volatility schematic
A small daily bell curve → √365 arrow → large annual bell curve with 1σ bands marked, plus a live readout of the exact calculation.
Volatility regime grid
Four regime cards (low, normal, high, extreme) with the card matching the current σ highlighted, so you can see where the reading sits at a glance.
Multi-horizon hints
Each field shows related quantities — daily, weekly, monthly, and annual σ, plus the implied 1σ price ranges at each horizon.
Distribution chart
A normal distribution of annual returns with 1σ and 2σ bands marked, showing exactly what the annualised volatility implies for the range of likely outcomes.
Volatility benchmarks
Reference tables covering typical σ by asset class, scaling factors for different trading calendars, and the four-regime interpretation framework.
Reference Tables & Conversions
A live volatility solver, a scaling lookup grid, and typical σ ranges by asset class.
Quick volatility annualiser
σ Scaling Lookup at σdaily = 2%
Computed from σh = σdaily · √(days in horizon). All values in %.
| Horizon | Days | √days | σ horizon | 1σ range (of horizon) |
|---|
Typical Volatility Ranges by Asset Class
Representative annualised σ values. Numbers are regime-dependent and shift with market conditions.
| Asset class | Typical annual σ | Approx. daily σ | Notes |
|---|---|---|---|
| Major FX pairs (EUR/USD) | 6 – 10% | 0.3 – 0.5% | Deepest, most liquid market in the world |
| Short-term US Treasuries | 1 – 3% | 0.05 – 0.15% | Near risk-free rate |
| Large-cap equity index (S&P 500) | 12 – 20% | 0.6 – 1.0% | Long-run average around 15% |
| Individual large-cap equity | 20 – 35% | 1.0 – 1.8% | Single-name volatility premium over index |
| Emerging market equity | 20 – 35% | 1.0 – 1.8% | Currency risk adds to equity risk |
| Gold | 12 – 18% | 0.6 – 0.9% | Moderate vol; low correlation to equities |
| Oil (WTI / Brent) | 25 – 45% | 1.3 – 2.4% | Cyclical; sensitive to supply shocks |
| Bitcoin (BTC) | 40 – 80% | 2.1 – 4.2% | Structural vol decline as market matures |
| Ethereum (ETH) | 50 – 90% | 2.6 – 4.7% | Slightly higher vol than BTC |
| Large-cap altcoins (SOL, AVAX) | 70 – 120% | 3.7 – 6.3% | Beta to BTC plus idiosyncratic risk |
| Small-cap altcoins / memecoins | 120 – 300% | 6.3 – 15.7% | Extreme; often dominated by narrative and illiquidity |
Scaling Factors for Different Trading Calendars
The annualisation factor depends on how many trading days the market has per year. Using the wrong factor is a common error.
| Market | Trading days per year | √days factor | Notes |
|---|---|---|---|
| Crypto (24/7/365) | 365 | 19.105 | Correct for BTC, ETH, and all crypto |
| US equities | 252 | 15.875 | Standard for SPX, NDX, single names |
| European equities | ~256 | 16.000 | Varies by exchange holiday calendar |
| FX | ~252 – 260 | ~15.9 – 16.1 | No weekend; holidays vary by currency |
| Futures (CME) | ~252 | 15.875 | Standard, matches equity calendar |
| Commodities | ~252 | 15.875 | Matches futures trading calendar |
| Bonds | ~252 | 15.875 | Standard; slight holiday variation |
Variable Reference
| Symbol | Meaning | Typical range | Units |
|---|---|---|---|
| σdaily | Daily standard deviation of log returns | 0.05 – 15 | % / day |
| σannual | Annualised volatility | 1 – 300 | % / yr |
| √365 | Annualisation factor (crypto) | 19.105 | — |
| √252 | Annualisation factor (equities) | 15.875 | — |
| σ² | Variance | σ squared | %² |
| 1σ range | One standard deviation band | ±σannual | % |
| 2σ range | Two standard deviation band | ±2σannual | % |
What Does σannual = σdaily · √365 Measure?
Volatility annualisation connects two quantities that every quant, options trader, and risk manager works with: the standard deviation of daily returns (σdaily, the raw statistical measurement) and the annualised volatility (σannual, the comparable figure used across markets and horizons). The scaling factor √365 is not a convention — it is a mathematical consequence of how variance scales with time, and getting it right (or wrong) is one of the most consequential details in quantitative finance.
Volatility Annualisation Formula
The defining relationship is:
Rearranged to solve for the other direction:
More generally, for any horizon of N days:
σannual = σdaily · √(days per year)
From these, additional metrics follow directly:
Monthly σ = σdaily · √30 = σdaily · 5.477
1σ price range = price · (1 ± σhorizon/100)
2σ price range = price · (1 ± 2σhorizon/100)
Volatility Variables
| Symbol | Meaning | Notes |
|---|---|---|
| σdaily | Daily volatility | Standard deviation of daily log returns over the sample |
| σannual | Annualised volatility | Standard quote for options, risk, and vol indices |
| σ² | Variance | Scales linearly with time; volatility scales with its square root |
| N | Horizon in days | Scaling factor is √N for any horizon |
| √365 | Annualisation factor (crypto) | ≈ 19.105; correct for 24/7/365 markets |
| √252 | Annualisation factor (equities) | ≈ 15.875; correct for markets that close on weekends |
How Each Variable Affects the Interpretation
The scaling factor determines the entire level of the annualised number, so using the wrong one is the single largest source of error in this calculation. Crypto trades every day, so √365 ≈ 19.105 is correct. Equities trade about 252 days a year, so √252 ≈ 15.875 is correct. Using √365 on equity data inflates annualised volatility by about 20%; using √252 on crypto data understates it by about 17%. The directional bias is systematic, not random, so it does not average out — it is a persistent error that distorts every downstream calculation that relies on σ, including option pricing, position sizing, and value-at-risk.
The choice of sample window matters almost as much. A 30-day window reacts to recent turbulence within days but is dominated by whatever happened in the last four weeks. A 90-day window smooths out short-term noise but lags regime changes by weeks. A 365-day window captures a full annual cycle but can entirely miss a recent sharp increase in volatility. Most professional desks compute multiple windows simultaneously and use the divergence between them as a signal: when 30-day σ is much higher than 90-day σ, recent turbulence has not yet propagated into the longer-term view, which often precedes mean reversion. When 30-day σ is much lower, the market may be complacent.
Finally, historical volatility is a descriptive statistic — it tells you what has happened, not what will happen. It is a factual measurement of the past. Implied volatility, by contrast, is what the options market is pricing for the future. The two usually diverge, and the size and sign of the divergence is itself a tradable signal. When IV is well above HV, the market is paying a premium for protection; when IV is well below HV, the market is underpricing risk. The "volatility risk premium" — the statistical tendency of IV to exceed HV on average — is one of the most robust empirical facts in finance, and it is why selling options systematically has historically been profitable, at least until the occasional catastrophic loss.
Volatility Calculation Examples
σannual = 2 · √365 = 2 · 19.105 = 38.21%
σannual = 2 · √252 = 2 · 15.875 = 31.75%
σdaily = 60 / √365 = 60 / 19.105 = 3.14%
σweekly = 2 · √7 = 2 · 2.646 = 5.29%
σmonthly = 2 · √30 = 2 · 5.477 = 10.95%
1σ range = $100 · (1 ± 0.40) = $60 to $140
Frequently Asked Questions
Because variance — the square of volatility — scales linearly with time, not volatility itself. If daily variance is σ_d², then N-day variance is N · σ_d². To get N-day volatility you take the square root of N-day variance, giving σ_d · √N. The annualisation factor is therefore √365 ≈ 19.105 for markets that trade every day. Using 365 directly (a factor of 365 instead of 19.1) would overstate annualised volatility by a factor of about 19, which is obviously wrong. The square-root rule is an approximation that assumes returns are independent and identically distributed, which is not strictly true in real markets — but it is accurate enough that it is used universally.
It depends on how many trading days the market has per year. Crypto trades 24/7/365, so use √365 ≈ 19.105. Equities, futures, FX, and bonds trade roughly 252 days a year (weekends plus holidays), so use √252 ≈ 15.875. Using the wrong factor is a material error: a 2% daily vol annualises to 38.21% under √365 but only 31.75% under √252 — a difference of over 6 percentage points. This calculator uses √365, which is correct for crypto. For equities you can either divide the result by √(365/252) ≈ 1.204 or set the trading-days field in the converter card above. Consistency matters most: pick one convention and stick with it.
Common choices are 30, 60, 90, and 365 days. A 30-day window is responsive to recent regime changes but noisy — a single extreme day can dominate it. A 90-day window is the standard compromise for medium-term analysis. A 365-day window gives a full-cycle view but lags recent shifts. Professional desks compute all three and watch the divergence: when 30-day σ is well above 90-day σ, recent turbulence has not yet propagated; when it is well below, the market may be complacent. For most purposes, 30-day is best for tactical decisions and 90-day for strategic ones. The sample window matters more than any other methodological choice, including the annualisation factor itself.
Historical volatility (HV) is backward-looking: it is computed from past returns and is a factual measurement of what has already happened. Implied volatility (IV) is forward-looking: it is derived from options prices using the Black-Scholes formula (or a comparable model) and represents the market's collective expectation of future volatility over the option's life. They usually diverge. When IV > HV, options are expensive and the market is pricing in future turbulence. When IV < HV, options are cheap and the market is complacent. The IV−HV spread is a tradable signal, and the "volatility risk premium" — the historical tendency of IV to exceed HV — is a well-documented empirical fact.
No. Volatility measures the magnitude of fluctuations, not their direction. A market with 40% annualised volatility could rise 40% or fall 40% over the year — the volatility is the same either way. This is why volatility is best understood as a measure of uncertainty or dispersion, not as a bull/bear signal. There is, however, a well-documented asymmetry: volatility tends to rise more during declines than during advances (the "leverage effect" or "volatility asymmetry"). Equities, in particular, tend to become more volatile when they fall, which is why vol is often called the "fear index." But that is a statistical tendency, not a rule, and it does not tell you which direction the next move will be — only that the next move is likely to be larger.
A common approach is "volatility targeting": size positions so that each one contributes a constant amount of risk to the portfolio. If your target is 15% annualised portfolio volatility and an asset has 40% annualised volatility, you would size the position at 15/40 = 37.5% of a fully-sized allocation. If the asset's volatility rises to 60%, you cut the position to 25%. This keeps portfolio risk roughly constant regardless of market conditions, and it has historically produced better risk-adjusted returns than fixed-weight sizing in trending markets. The key input is the volatility forecast, which is usually a blend of recent HV, longer-term HV, and market IV. Getting the σ right matters directly — a 20% error in σ translates into a 20% error in position size.
Several factors compound. Crypto markets are younger and less mature, so price discovery is less efficient and narratives dominate fundamentals. They have no earnings, no dividend, no cash flow — valuation is entirely reflexive, driven by what the next buyer will pay. They trade 24/7 without circuit breakers, so tail events can extend further before halting. They have thinner liquidity at the aggregate level, so relatively small flows move prices more. They have high retail participation, which amplifies sentiment swings. And they are subject to regulatory shocks, exchange failures, and protocol exploits that have no direct parallel in equities. The result is annualised volatility in the 40–80% range for BTC, 50–90% for ETH, and 100%+ for smaller tokens — roughly 3–10× the volatility of large-cap equities. As the market matures, most analysts expect crypto vol to compress gradually, but it is unlikely to ever match equity vol because the structural features above are unlikely to disappear entirely.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| σ_annual | Annualized volatility | % |
| σ_daily | Daily standard deviation of returns | % |
What it means
Historical volatility is the standard deviation of returns over a period. Annualising daily volatility assumes independence and is used to compare volatility across different time frames. This is used in risk management and in option pricing. Understanding volatility is essential for traders and investors to assess market conditions and to set position sizes. High volatility indicates greater risk.
Worked example
Historical Volatility – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| Daily Volatility (%) | 3.5 |
| Parameter | Value |
|---|---|
| Daily Volatility | 2.0% |
Common mistakes
- Annualised volatility: σ_annual = σ_daily × √(365) (or √(252) for trading days).
- σ_daily: Standard deviation of daily returns.
- √365: Assumes calendar days – use √252 for business days.
- Volatility: A key input for risk models.
Applications
Historical volatility (annualized) converts daily volatility to an annualised figure, scaling by the square root of trading days. This is used to measure the price fluctuation of an asset. Investors and traders use it to gauge risk, to price options, and to set position sizes. Higher volatility indicates greater uncertainty. Understanding historical volatility is essential for risk management and for derivatives pricing.
- Measuring the risk and uncertainty of an asset
- Setting position sizes and stop‑loss levels
- Option pricing and implied volatility comparison
- Assessing market sentiment and regime
- Educational understanding of volatility
Related calculators · Technical & Market Analysis
Recently updated formulas
Suggest an improvement
Found a mistake? Have a better example? Let us know.
You may send up to 3 suggestions per 24 hours.